Flagpole Question

Question

Bob, who is 2.2 m tall, is standing a distance of 15 m from a flagpole. From his point of view, the angle of view between the top and bottom of the pole is 32 degrees. How tall is the flagpole to the nearest hundredth of a metre?

Answer 1

Draw a line from Bob's view point to the base of the flag pole to form a right triangle. Let θ be the angle from the ground to Bob's view point.

tan(θ) = 2.2/15

θ = tan^-1(2.2/15) ≈ 8.34°.

The complimentary angle to θ is 90-θ ≈ 81.66°.

The angle measurements of the triangle formed by Bob's view point and the flagpole are 32°, 81.66° and 66.34° which add up to 180°.

Draw a horizontal line from Bob's view point to the flagpole. Let x be the length from the intersection of that line and the flagpole to the top of the flagpole, such that x+2.2 is the height of the flagpole.

tan(66.34) = 15/x

x = 15/tan(66.34) = 15/2.28 ≈ 6.57

6.57 + 2.2 = 8.77 meters